PreprintarXiv licencearXiv
On the causality of gravitational pp-wave spacetimes: A null version of Anderson's rigidity theorem
Abstract
We prove that plane waves are the only gravitational pp-wave spacetimes which are distinguishing; in particular, they are the only strongly causal ones. This is used to prove a null version of Anderson's rigidity theorem, conjectured by Costa e Silva and Flores: every geodesically complete, transversally complete, strongly causal, Ricci-flat Brinkmann spacetime of dimension $4$ is isometric to a quotient of a plane wave spacetime.
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BibTeX
@misc{cairo2026causality,
title = {{On the causality of gravitational pp-wave spacetimes: A null version of Anderson's rigidity theorem}},
author = {Hannah Cairo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03749},
eprint = {2610.03749},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03749},
}
RIS
TY - UNPB
TI - On the causality of gravitational pp-wave spacetimes: A null version of Anderson's rigidity theorem
AU - Hannah Cairo
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.03749
UR - https://arxiv.org/abs/2610.03749
AB - We prove that plane waves are the only gravitational pp-wave spacetimes which are distinguishing; in particular, they are the only strongly causal ones. This is used to prove a null version of Anderson's rigidity theorem, conjectured by Costa e Silva and Flores: every geodesically complete, transversally complete, strongly causal, Ricci-flat Brinkmann spacetime of dimension $4$ is isometric to a quotient of a plane wave spacetime.
ER -